Sign up to receive free email alerts when patent applications with chosen keywords are publishedSIGN UP

Abstract:

There is provided a graph display apparatus. An image display control
unit causes a display unit to display the image data stored by the image
and graph formula storage unit. An formula input unit inputs a graph
formula according to a user operation. An input graph display control
unit causes the display unit to display a graph corresponding to a graph
formula input by the formula input unit, on the image data displayed on
the display unit by the image display control unit as a background image.
A model graph display control unit causes the display unit to display, in
a different display mode, a graph corresponding to a model graph formula
stored by the image and graph formula storage unit, together with the
graph displayed on the image data as the background image on the display
unit by the input graph display control unit, according to a user
operation.

Claims:

1. A graph display apparatus comprising: an image and graph formula
storage unit configured to store image data and a model graph formula
corresponding to the image data; an image display control unit configured
to cause a display unit to display the image data stored by the image and
graph formula storage unit; an formula input unit configured to input a
graph formula according to a user operation; an input graph display
control unit configured to cause the display unit to display a graph
corresponding to a graph formula input by the formula input unit, on the
image data displayed on the display unit by the image display control
unit as a background image; and a model graph display control unit
configured to cause the display unit to display, in a different display
mode, a graph corresponding to a model graph formula stored by the image
and graph formula storage unit, together with the graph displayed on the
image data as the background image on the display unit by the input graph
display control unit, according to a user operation.

2. The graph display apparatus according to claim 1, further comprising a
graph formula list display unit configured to display, in list form, a
model graph formula stored by the image and graph formula storage unit
and a graph formula input by the formula input unit in different display
modes, wherein a graph corresponding to the graph formula displayed by
the input graph display control unit and a graph corresponding to the
model graph formula displayed by the model graph display control unit are
displayed in the same display modes as those of the respective
corresponding graph formulas displayed by the graph formula list display
unit.

3. The graph display apparatus according to claim 1, wherein the image
and graph formula storage unit stores image data, a coefficient-added
model graph formula corresponding to the image data, its coefficient
values, and approximation ranges of the coefficient values, the formula
input unit inputs a coefficient-added graph formula and its coefficient
values according to a user operation, and the graph display apparatus
further comprises a coefficient value determination display control unit
configured to determine whether the coefficient values of the
coefficient-added graph formula input by the formula input unit coincide
with, approximate, or differ from the coefficient values of the
coefficient-added model graph formula on the basis of the
coefficient-added model graph formula, its coefficient values, the
approximation ranges of the coefficient values stored by the image and
graph formula storage unit and configured to cause the display unit to
display a determination result.

4. The graph display apparatus according to claim 1, further comprising:
a coincidence degree determination unit configured to determine a degree
of coincidence of the model graph formula stored by the image and graph
formula storage unit with a graph formula input by the formula input
unit; and a coincidence degree display control unit configured to cause
the display unit to display the degree of coincidence of the model graph
formula with the input graph formula determined by the coincidence degree
determination unit.

5. The graph display apparatus according to claim 1, further comprising:
a display setting unit configured to set inhibition or permission of a
change of a display range of a graph displayed on the image data as the
background image on the display unit by the model graph display control
unit, according to a user operation; a display range change specifying
unit configured to specify the change of the display range of a graph
according to a user operation; and a change inhibition display control
unit configured to cause the display unit to display information that the
change of the display range is inhibited if the inhibition of the change
of the display range is set by the display setting unit when the change
of the display range of a graph is specified by the display range change
specifying unit.

6. A graph display method for use in a graph display apparatus including
a display unit, an input unit, and an image and graph formula storage
unit configured to store image data and a model graph formula
corresponding to the image data, the method comprising: performing an
image display control process to cause the display unit to display image
data stored by the image and graph formula storage unit; performing a
formula input process to input a graph formula according to a user
operation on the input unit; performing an input graph display control
process to cause the display unit to display a graph corresponding to a
graph formula input by the formula input process, on the image data
displayed on the display unit by the image display control process as a
background image; and performing a model graph display control process to
cause the display unit to display, in a different display mode, a graph
corresponding to a model graph formula stored by the image and graph
formula storage unit, together with the graph displayed on the image data
as the background image on the display unit by the input graph display
control process.

7. The method according to claim 6, further comprising performing a graph
formula list display process to display, in list form, a model graph
formula stored by the image and graph formula storage unit and a graph
formula input by the formula input process in different display modes,
wherein a graph corresponding to the graph formula displayed by the input
graph display control process and a graph corresponding to the model
graph formula displayed by the model graph display control process are
displayed in the same display modes as those of the respective
corresponding graph formulas displayed by the graph formula list display
process.

8. The method according to claim 6, wherein the image and graph formula
storage unit stores image data, a coefficient-added model graph formula
corresponding to the image data, its coefficient values, and
approximation ranges of the coefficient values, the formula input process
comprises inputting a coefficient-added graph formula and its coefficient
values according to a user operation, and the method further comprises
performing a coefficient value determination display control process to
determine whether the coefficient values of the coefficient-added graph
formula input by the formula input process coincide with, approximate, or
differ from the coefficient values of the coefficient-added model graph
formula on the basis of the coefficient-added model graph formula, its
coefficient values, the approximation ranges of the coefficient values
stored by the image and graph formula storage unit and to cause the
display unit to display a determination result.

9. The method according to claim 6, further comprising: performing a
coincidence degree determination process to determine a degree of
coincidence of the model graph formula stored by the image and graph
formula storage unit with a graph formula input by the formula input
process; and performing a coincidence degree display control process to
cause the display unit to display the degree of coincidence of the model
graph formula with the input graph formula determined by the coincidence
degree determination process.

10. The method according to claim 6, further comprising: performing a
display setting process to set inhibition or permission of a change of a
display range of a graph displayed on the image data as the background
image on the display unit by the model graph display control process,
according to a user operation; performing a display range change
specifying process to specify the change of the display range of a graph
according to a user operation; and performing a change inhibition display
control process to cause the display unit to display information that the
change of the display range is inhibited if the inhibition of the change
of the display range is set by the display setting process when the
change of the display range of a graph is specified by the display range
change specifying process.

11. A computer-readable storage medium having a program stored thereon
for use in a computer as a graph display apparatus including a display
unit, an input unit, and an image and graph formula storage unit
configured to store image data and a model graph formula corresponding to
the image data, the program causing the computer to perform: an image
display control process to cause the display unit to display image data
stored by the image and graph formula storage unit; a formula input
process to input a graph formula according to a user operation on the
input unit; an input graph display control process to cause the display
unit to display a graph corresponding to a graph formula input by the
formula input process, on the image data displayed on the display unit by
the image display control process as a background image; and a model
graph display control process to cause the display unit to display, in a
different display mode, a graph corresponding to a model graph formula
stored by the image and graph formula storage unit, together with the
graph displayed on the image data as the background image on the display
unit by the input graph display control process.

12. The storage medium according to claim 11, wherein the program causes
the computer to further perform a graph formula list display process to
display, in list form, a model graph formula stored by the image and
graph formula storage unit and a graph formula input by the formula input
process in different display modes, wherein a graph corresponding to the
graph formula displayed by the input graph display control process and a
graph corresponding to the model graph formula displayed by the model
graph display control process are displayed in the same display modes as
those of the respective corresponding graph formulas displayed by the
graph formula list display process.

13. The storage medium according to claim 11, wherein the image and graph
formula storage unit stores image data, a coefficient-added model graph
formula corresponding to the image data, its coefficient values, and
approximation ranges of the coefficient values, the formula input process
comprises inputting a coefficient-added graph formula and its coefficient
values according to a user operation, and the program causes the computer
to further perform a coefficient value determination display control
process to determine whether the coefficient values of the
coefficient-added graph formula input by the formula input process
coincide with, approximate, or differ from the coefficient values of the
coefficient-added model graph formula on the basis of the
coefficient-added model graph formula, its coefficient values, the
approximation ranges of the coefficient values stored by the image and
graph formula storage unit and to cause the display unit to display a
determination result.

14. The storage medium according to claim 11, wherein the program causes
the computer to further perform: a coincidence degree determination
process to determine a degree of coincidence of the model graph formula
stored by the image and graph formula storage unit with a graph formula
input by the formula input process; and a coincidence degree display
control process to cause the display unit to display the degree of
coincidence of the model graph formula with the input graph formula
determined by the coincidence degree determination process.

15. The storage medium according to claim 11, wherein the program causes
the computer to further perform: a display setting process to set
inhibition or permission of a change of a display range of a graph
displayed on the image data as the background image on the display unit
by the model graph display control process, according to a user
operation; a display range change specifying process to specify the
change of the display range of a graph according to a user operation; and
a change inhibition display control process to cause the display unit to
display information that the change of the display range is inhibited if
the inhibition of the change of the display range is set by the display
setting process when the change of the display range of a graph is
specified by the display range change specifying process.

Description:

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application is based upon and claims the benefit of priority
from prior Japanese Patent Application No. 2010-095405, filed Apr. 16,
2010, the entire contents of which are incorporated herein by reference.

BACKGROUND OF THE INVENTION

[0002] 1. Field of the Invention

[0003] The present invention relates to a graph display apparatus, a graph
display method, and a storage medium storing a program, capable of
displaying, for example, the trajectory of a moving body included in a
captured image in graph form for a learning purpose.

[0004] 2. Description of the Related Art

[0005] To support a person's learning, an electronic computer system, such
as a client-server system, has been used.

[0006] For example, a learning server creates question information
according to the learning progress of each learner and displays the
information on a learning terminal. Then, the learning server makes a
true-false judgment on the basis of answer information sent from the
learning terminal and displays the question information repeatedly until
the answer is passed. By doing this, a conventional learning-support
system enables a learner not only to learn according to the learner's
learning progress but also to continue motivation for learning.

[0007] For example, the trajectory of a ball or a fountain included in a
composite image consecutively captured was analyzed in graph form. To
learn its graph formula, only an evaluation of a correct or an incorrect
answer was output, depending on whether the graph formula input as an
answer by the learner coincided with a correct graph formula previously
stored.

[0008] Therefore, the following problem arose: the learner could not try
to input a graph formula as an answer repeatedly, while checking how much
a graph corresponding to a learner-input graph formula differed from a
dynamic trajectory to be analyzed on the image or a correct graph, which
prevented effective learning.

BRIEF SUMMARY OF THE INVENTION

[0009] Accordingly, it is an object of the invention to provide a graph
display apparatus, a graph display method, and a storage medium storing a
program, which enable a user to check the difference between a graph
corresponding to a graph formula input by the user and its correct answer
on an image when analyzing a dynamic trajectory on the image and learn
the graphs effectively and a control program for the graph display
apparatus.

[0010] According to one aspect of the invention, there is provided a graph
display apparatus comprising: an image and graph formula storage unit
configured to store image data and a model graph formula corresponding to
the image data; an image display control unit configured to cause a
display unit to display the image data stored by the image and graph
formula storage unit; an formula input unit configured to input a graph
formula according to a user operation; an input graph display control
unit configured to cause the display unit to display a graph
corresponding to a graph formula input by the formula input unit, on the
image data displayed on the display unit by the image display control
unit as a background image; and a model graph display control unit
configured to cause the display unit to display, in a different display
mode, a graph corresponding to a model graph formula stored by the image
and graph formula storage unit, together with the graph displayed on the
image data as the background image on the display unit by the input graph
display control unit, according to a user operation.

[0011] Additional objects and advantages of the invention will be set
forth in the description which follows, and in part will be obvious from
the description, or may be learned by practice of the invention. The
objects and advantages of the invention may be realized and obtained by
means of the instrumentalities and combinations particularly pointed out
hereinafter.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING

[0012] The accompanying drawings, which are incorporated in and constitute
a part of the specification, illustrate embodiments of the invention, and
together with the general description given above and the detailed
description of the embodiments given below, serve to explain the
principles of the invention.

[0013]FIG. 1 shows an external configuration of a graph function
calculator according to an embodiment of a graph display apparatus of the
invention;

[0014]FIG. 2 is a block diagram showing a configuration of the electronic
circuitry of the graph function calculator 10;

[0015]FIG. 3 is a table showing the contents of an "Images & Coordinate
setting & Graph formulas" file stored in a file database 22F of the graph
function calculator 10;

[0016]FIG. 4 is a flowchart to explain a function graph display process
(part 1) performed by the graph function calculator 10;

[0017]FIG. 5 is a flowchart to explain a function graph display process
(part 2) performed by the graph function calculator 10;

[0024] Hereinafter, referring to the accompanying drawings, embodiments of
the invention will be explained.

[0025]FIG. 1 shows an external configuration of a graph function
calculator 10 according to an embodiment of a graph display apparatus of
the invention.

[0026] The graph function calculator 10 is in a small size that enables
the user to hold it easily in one hand and operate it with one hand. On
the front face of the body of the graph function calculator 10, there are
provided a key input unit 11 and a color display unit 16.

[0027] The key input unit 11 includes a numeric and operation symbol key
group 12 for inputting numbers and formulas and giving instructions to do
calculations, a function key group 13 for inputting various functions, a
mode setting key group 14 for displaying menu screens for various
operation modes and giving instructions to set an operation mode, a
cursor key 15 for moving a cursor displayed on the color display unit 16
and selecting data items, and function keys F1 to F6 for selectively
specifying various functions that are printed on the key panel or
displayed in menu form along the lower end of the color display unit 16.

[0031] On the key panel along the upper edge of each of the keys, an
available character, symbol, function, or functional capability is
printed. Each of them can be entered by combining SHIFT key in the mode
setting key group 14 with the corresponding key.

[0032] For example, the MENU key combined with SHIFT key functions as SET
UP key and can give an instruction to switch to a graph display setting
screen G3 (FIG. 9A).

[0033] The color display unit 16 includes a dot-matrix color
liquid-crystal display unit. On its display screen, a transparent-tablet
touch panel 16T for detecting a touch position on the screen is laid.

[0034] The graph function calculator 10 has the function of causing the
color display unit 16 to display a graph image composition screen GK with
a graph according to a preset coordinate range being laid on an image
previously captured in the background. The graph image composition screen
GK has the function of displaying, in different display colors, for
example, graphs Y1, Y3 corresponding to graph formulas input by the user
and graph Y2 corresponding to a prepared model formula according to
trajectories b1 to b7 of a moving body to be analyzed.

[0035]FIG. 2 is a block diagram showing a configuration of the electronic
circuitry of the graph function calculator 10. The graph function
calculator 10 includes a processor (CPU) 21 of a computer.

[0036] The processor (CPU) 21 controls the operations of various parts of
the circuit according to a system program previously stored in a memory
(flash ROM) 22, a calculator control program read from an external
recording medium 23, such as a memory card, into the memory 22 via a
recording medium readout unit 24, or a calculator control program
downloaded from a Web server (program server) on a communication network,
such as the Internet, by a PC communication unit 25 via an external PC 30
and read into the memory 22. Then, the system program or calculator
control program previously stored in the memory 22 is activated in
response to a key input signal from the key input unit 11 or a touch
position detect signal from the touch panel 16T.

[0038] The memory (flash ROM) 22 stores, as a calculator control program,
an arithmetic processing program for performing arithmetic processing
according to an arbitrary formula input by the user from the key input
unit 11, a graph drawing program for performing graph drawing according
to an arbitrary function expression input by the user, a function graph
displaying program 22a for displaying, in learning form, the relationship
between the trajectory of a moving body in a prepared image and a graph
according to a preset coordinate range, and others.

[0043] The model formula memory 22e stores, together with coefficient
values and their allowable ranges, a graph formula Y=f(x) acting as a
model in executing the function graph displaying program 22a.

[0045] The full color analysis image memory 22g stores, in full color
resolution, image data set as an analysis object in executing the
function graph displaying program 22a.

[0046] The color graph image memory 22h stores graph image data
corresponding to a user graph formula stored in the graph formula data
memory 22b and graph image data corresponding to a model graph formula
stored in the model formula memory 22e as color image data on the basis
of the coordinate range and its scale value stored in the V-Window
setting value memory 22c and various display setting data
([Grid][Axes][Label][V-W Lock] and the like) stored in the SET UP data
memory 22d.

[0047] The graph image composition screen GK displayed on the color
display unit 16 according to the function graph displaying program 22a is
created by laying the graph image data stored in the color graph image
memory 22h on the image data stored in the full color analysis image
memory 22g in the background.

[0048]FIG. 3 is a table showing the contents of an "Images & Coordinate
setting & Graph formulas" file stored in a file database 22F of the graph
function calculator 10.

[0049] The "Images & Coordinate setting & Graph formulas" file is created
previously at, for example, the external PC 30 and loaded into the file
database 22F of the graph function calculator 10. Alternatively, image
data is externally loaded and coordinate setting data and graph formula
data are created by the graph function calculator 10. Then, the image
data and the graph formula data are stored in the file database 22F.

[0050] For example, a file caused to correspond to file name BASKET.g3m
stores composite image data of consecutive images in shooting a goal in a
basketball game, coordinate setting data includes a coordinate range, its
scale values, and display setting data ([Grid][Axes][Label][V-W Lock],
and the like), and graph formula data on a graph formula corresponding to
a trajectory of a moving body in the composite image.

[0051] In the case of a file caused to correspond to file name BALL.g3m,
graph formula data includes a graph formula with coefficients, individual
coefficient values, and their allowable ranges.

[0052] Next, a function graph displaying function of the graph function
calculator 10 configured as described above will be explained.

[0053]FIG. 4 is a flowchart to explain a function graph display process
(part 1) performed by the graph function calculator 10.

[0054]FIG. 5 is a flowchart to explain a function graph display process
(part 2) performed by the graph function calculator 10.

[0056] FIGS. 7A to 7D are diagrams showing display operations (part 1) of
a first embodiment in a function graph display process of the graph
function calculator 10.

[0057] FIGS. 8A to 8E are diagrams showing display actions (part 2) of the
first embodiment in the function graph display process of the graph
function calculator 10.

[0058] FIGS. 9A to 9C are diagrams showing display actions (part 3) of the
first embodiment in the function graph display process of the graph
function calculator 10.

[0059] When "Picture Graph" for creating a graph image composition screen
GK has been selected from an operation mode menu screen displayed on the
color display unit 16 according to the operation of the MENU key at the
key input unit 11 and FILE has been specified from a menu displayed in
the lower part of the screen according to the operation of function key
Fn, a file selection screen G1 for selecting a desired file from "Image &
Coordinate setting & Graph formulas" files 1, 2 stored in the file
database 22F of the memory 22 is displayed as shown in FIG. 7A (step S1).

[0060] On the file selection screen G1, when file name BASKET.g3m (FIG. 3)
desired by the user has been selected with the cursor Cu and OPEN has
been selected according to the operation of function key F1, an image in
the selected file BASKET.g3m has been read and written into the full
color analysis image memory 22g and displayed on the color display unit
16 as a background image as shown in FIG. 7B (step S2).

[0061] At this time, a graph coordinate system has not been displayed yet.

[0062] In addition, coordinate setting data in the selected file
BASKET.g3m has been read and set in the V-Window setting value memory 22c
and SET UP data memory 22d of the memory 22 (step S3).

[0063] At this time, a graph coordinate system corresponding to the
coordinate setting data ([coordinate range (Xmin=-1.0277 to Xmax=9.4272,
Ymin=-0.4722 to Ymax=4.6944)] [scale values (X=0.5, Y=1)] [Grid:Line
(line display)] [Axes:Scale (scale & numeric display)] [Label: On
(display of origin and coordinate axis names x, y)] [V-W Lock: On (no
range change)]) (FIG. 3) is written in the color graph image memory 22h
and superimposed on an image of BASKET.g3m already displayed as a
background image as shown in FIG. 7B, which is displayed as a graph image
composition screen GK on the color display unit 16.

[0064] If a graph image composition screen GK where the graph coordinate
system written in the color graph image memory 22h has been actually
superimposed on the image written in the full color analysis image memory
22g is shown diagrammatically, it will look complicated and be difficult
to understand. Therefore, FIG. 7B separately shows a screen on which the
image is displayed and a screen on which the graph coordinate system is
displayed. The same holds true for the rest.

[0065] Next, graph formula data in the selected file BASKET.g3m is read
and set in the model formula memory 22e of the memory 22 (step S4).

[0066] When [GT] (switching between a graph and an formula) has been
specified according to the operation of function key F6 to analyze
trajectories b1 to b7 of a moving body (in this case, a ball) included in
the graph image composition screen GK from the graph, control is passed
to a graph formula input process of FIG. 6 (step SA). First, as shown in
FIG. 7C, a graph formula list screen G2 which lists the individual graph
formulas stored in the graph formula data memory 22b and model formula
memory 22e is displayed on the color display unit 16 (step A1).

[0067] Here, when it has been determined that a model (model answer) has
been set because graph formula data Y2=-0.4(X-2.5)2+4.5 (FIG. 3) in
the selected file BASKET.g3m has been set in the model formula memory 22e
(Yes in step A2), graph formula Y2 for the model is displayed so as to be
covered with mask M represented as <<Model>> (step A3).

[0068] In the individual graph formulas listed on the graph formula list
screen G2, graph formula Y1 is identified by blue, Y2 by red, Y3 by
green, Y4 by pink, and Y5 by black. Y6 and subsequent formulas are
identified by the repetition of these colors. Of them, a graph formula
selected by cursor Cu as an input target (in this case, Y1') is
identified by black.

[0069] Then, if it has been determined that model graph formula Y2
[Y2=-0.4(X-2.5)2+4.5] covered with mask M is not a graph formula
with coefficients (No in step A4), control goes into a state where a
graph formula is to be input according to a user operation.

[0070] Here, if graph formula Y1 [Y1=-0.5(X-3)2+4] the user came up
with has been input and displayed as shown in FIG. 7C on the basis of
moving body trajectories b1 to b7 on the graph image composition screen
GK (FIG. 7B) displayed on the color display unit 16 according to steps S1
to S4, the graph formula Y1 is stored in the graph formula data memory
22b (step A5).

[0071] Then, if [GT] (switching between a graph and an formula) has been
specified according to the operation of function key F6 as shown in FIG.
7D to display a graph corresponding to the user-input graph formula Y1
[Y1=-0.5(X-3)2+4] on the graph image composition screen GK, it is
determined that the input of the graph formula has been completed (No in
step A6→Yes in step A7) and that graph drawing has been specified
(Yes in step S5).

[0072] Then, a graph coordinate system corresponding to coordinate setting
data (FIG. 3) in file No. 1 set in the V-Window setting value memory 22c
and SET UP data memory 22d is drawn on the color graph image memory 22h.
At the same time, graph Y1 corresponding to the user-input graph formula
Y1=-0.5(X-3)2+4 is drawn in blue, the display color of graph Y1,
according to the drawn graph coordinate system. Then, the image of graph
Y1 drawn on the color graph image memory 22h is superimposed on the image
of file No. 1 already drawn as a background image on the full color
analysis image memory 22g, thereby displaying the resulting image as a
graph image composition screen GK on the color display unit 16 (step S6).

[0073] In FIG. 7D, although graph Y1 is not drawn directly on the full
color analysis image memory 22g on which the background image of file No.
1 has been drawn, the graph image composition screen GK shows how graph
Y1 is combined with the moving body trajectories b1 to b7.

[0074] When the user has determined on the basis of the graph image
composition screen GK displayed on the color display unit 16 that the
difference between the moving body trajectories b1 to b7 and graph Y1 is
great and therefore specified [GT] (switching between a graph and an
formula) according to the operation of the function key F6 to add graph
Y3, control is passed again to the graph formula input process of FIG. 6
(No in step S5→Yes in step S7→step SA) and a graph formula
list screen G2 is displayed on the color display unit 16 as shown in FIG.
8A (step A1).

[0075] As in the previous graph formula input process, since it has been
determined that a model (model answer) has been set because graph formula
data Y2=-0.4(X-2.5)2+4.5 (FIG. 3) in the selected file BASKET.g3m
has been set in the model formula memory 22e (Yes in step A2), graph
formula Y2 for the model is displayed so as to be covered with mask M
represented as <<Model>> (step A3).

[0076] In addition, since it has been determined that model graph formula
Y2 [Y2=-0.4(X-2.5)2+4.5] covered with mask M is not a graph formula
with coefficients (No in step A4), control goes into a state where a
graph formula is to be input according to a user operation.

[0077] Here, if a new graph formula Y3 [Y3=-0.4(X-4)2+5] the user
came up with has been input and displayed as shown in FIG. 8A on the
basis of moving body trajectories b1 to b7 on the graph image composition
screen GK (FIG. 7D) displayed on the color display unit 16, the graph
formula Y3 is stored in the graph formula data memory 22b (step A5).

[0078] Then, if the EXE (execution) key 12b has been pressed as shown in
FIG. 8B to additionally display graph formula Y3 [Y3=-0.4(X-4)2+5]
newly input by the user on the graph image composition screen GK, it is
determined that the input of the graph formula is complete (No in step
A6→Yes in step A7) and that graph drawing has been specified (Yes
in step S5).

[0079] Then, a graph coordinate system corresponding to coordinate setting
data (FIG. 3) in file No. 1 set in the V-Window setting value memory 22c
and SET UP data memory 22d is drawn again on the color graph image memory
22h. At the same time, graph Y1 corresponding to the user-input graph
formula Y1=-0.5(X-3)2+4 is drawn in blue, the display color of graph
Y1, and graph Y3 corresponding to graph formula Y3=-0.4(X-4)2+5 is
drawn in green, the display color of graph Y3, according to the drawn
graph coordinate system. Then, the images of graphs Y1 and Y3 drawn on
the color graph image memory 22h are superimposed on the image of file
No. 1 already drawn as a background image on the full color analysis
image memory 22g, thereby displaying the resulting image as a graph image
composition screen GK on the color display unit 16 (step S6).

[0080] When the user has determined on the basis of the graph image
composition screen GK displayed on the color display unit 16 that the
difference between moving body trajectories b1 to b7 and graph Y3 is
still great and therefore specified [GT] (switching between a graph and
an formula) according to the operation of function key F6 to refer to
model (model answer) graph formula Y2, control is passed again to the
graph formula input process of FIG. 6 (No in step S5→Yes in step
S7→step SA) and a graph formula list screen G2 is displayed on the
color display unit 16 as shown in FIG. 8C (step A1).

[0081] In the graph formula list screen G2, the equal sign = in each of
graph formulas Y1, Y3 corresponding to the graph already displayed as the
graph image composition screen GK is identified in reversed display h.

[0082] Here, when cursor. Cu is moved to the position of model graph
formula Y2 covered with mask M, mask M is erased and model graph formula
Y2 [Y2=-0.4(X-2.5)2+4.5] becomes visible and is set as a target
formula in graph display (Yes in steps A2 to A6→step A8).

[0083] Then, as shown in FIG. 8D, when the EXE key has been pressed, it is
determined that the input of the graph formula is complete (Yes in step
A7) and that graph drawing has been specified (Yes in step S5).

[0084] Then, a graph coordinate system corresponding to coordinate setting
data (FIG. 3) in file No. 1 set in the V-Window setting value memory 22c
and SET UP data memory 22d is drawn again on the color graph image memory
22h. At the same time, graph Y1 corresponding to the user-input graph
formula Y1=-0.5(X-3)2+4 is drawn in blue, the display color of graph
Y1, graph Y3 corresponding to graph formula Y3=-0.4(X-4)2+5 is drawn
in green, the display color of graph Y3, and graph Y2, corresponding to
graph formula Y2=-0.4(X-2.5)2+4.5 is drawn in red, the display color
of graph Y2 according to the drawn graph coordinate system. Then, the
images of graphs Y1, Y2, and Y3 drawn on the color graph image memory 22h
are superimposed on the image of file No. 1 already drawn as a background
image on the full color analysis image memory 22g, thereby displaying the
resulting image as a graph image composition screen GK on the color
display unit 16 (step S6).

[0085] As described above, the coordinate system according to the preset
range setting data and display setting data is combined with captured
full color images trajectories b1 to b7 of a moving body to be analyzed
and the resulting image is displayed. At the same time, graphs Y1, Y3
corresponding to the respective graph formulas input by the user to
analyze the trajectories b1 to b7 of the moving body according to the
coordinate system are combined using the display colors of the respective
graph formulas, that is, blue and green, and the resulting image is
displayed. Then, when the model (model answer) graph formula previously
input so as to correspond to the trajectories b1 to b7 of the moving body
to be analyzed has been specified, graph Y2 corresponding to the model
graph formula is also combined in red, the display color of the graph
formula, for identification.

[0086] Accordingly, when a dynamic trajectory in an image is analyzed, the
user can learn effectively, while checking the difference between a graph
based on the user-input graph formula and its correct answer on the
image.

[0087] Then, to see the feature points and the like of graphs Y1, Y2, Y3
drawn on the color graph image memory 22h by scrolling the graphs and the
coordinate system in an arbitrary direction on the graph image
composition screen GK of FIG. 8D, if the user has pressed the →
cursor key pointing at the direction in which the user wants to scroll
the coordinate system as shown in FIG. 8E, it is determined that the
movement of the graph has been specified (Yes in step S8).

[0088] Then, it is determined whether [V-W Lock] in the display setting
data set in the SET UP data memory 22d is On (no range change) or Off
(changeable), that is, whether display is locked or not (step S9).

[0089] Here, if it has been determined that [V-W Lock] in the display
setting data set in the SET UP data memory 22d is On (no range change)
and display is locked (Yes in step S9), error message "V-Window is
locked" E meaning that display is being locked is drawn on the graph
image in the color graph image memory 22h, which is displayed as a graph
image composition screen GE (step S10→step S6).

[0090] Then, when [Set up] (display setting) has been specified according
to the operation of the SHIFT+MENU keys (Yes in step S11), a display
setting screen G3 for changing the display setting data set in the SET UP
data memory 22d according to a user operation is displayed on the color
display unit 16 as shown in FIG. 9A (step S12).

[0091] On the display setting screen G3, when cursor Cu has been moved to
item [V-Window Lock] for setting whether display is locked and item [off]
displayed at the lower end of the screen has been selected according to
the operation of function key F2 as shown in FIG. 9B, the set contents in
item [V-Window Lock] are changed from On to Off (step S13).

[0092] Then, when the EXE key is pressed, the changed display setting data
is set in the SET UP data memory 22d and it is determined that the
setting is complete (Yes in step S14) and the same graph image
composition screen GK as that before the display setting data was changed
is drawn and displayed on the color display unit 16 (Yes in step
S5→step S6).

[0093] Here, if the → cursor key pointing in a direction in which
the user wants to scroll the graph image has been operated again as shown
in FIG. 9C and it has been determined that the movement of the graph has
been specified (Yes in step S8), it is determined that display has not
been locked because item [V-W Lock] in the display setting data set in
the SET UP data memory 22d is Off (changeable) (No in step S9).

[0094] Then, the coordinate range (Xmin to Xmax, Ymin to Ymax) of the
color display unit 16 stored in the V-Window setting value memory 22c is
changed according to the operation of the → cursor key 15 (step
S15) and a coordinate system scrolled according to the changed coordinate
range and graphs Y1, Y2, Y3 corresponding to the respective graph
formulas are drawn on the color graph image memory 22h. Then, a graph
image composition screen GK obtained by superimposing the scrolled graph
image on a background image drawn on the full color analysis image memory
22g is displayed on the color display unit 16 (Yes in step S5→step
S6).

[0095] At this time, on the graph image composition screen GK, a graph
image including the coordinate system drawn on the color graph image
memory 22h is scrolled in an arbitrary direction selected by the user and
displayed, whereas the background image drawn on the full color analysis
image memory 22g is not scrolled and therefore there is a difference
between the moving body trajectories b1 to b7 included in the background
image and a graph corresponding to model graph formula Y2.

[0096] As described above, when item [V-W Lock] in the display setting
data whose setting can be changed arbitrarily by the user has been set to
On on the graph image composition screen OK obtained by superimposing the
graph image drawn on the color graph image memory 22h on the background
image drawn on the full color analysis image memory 22g, scroll display
involving the coordinate range of the graph image being moved and changed
can be inhibited. When item [V-W Lock] has been set to Off, scroll
display involving the coordinate range of the graph image being moved and
changed can be performed freely.

[0097] Furthermore, when item [V-W Lock] in the display setting data has
been set to On, display change involving the coordinate range of the
graph image being expanded or narrowed is also inhibited (Yes in step
S16→Yew in step S17→S10). In addition, when item [V-W Lock]
has been set to Off, display change involving the coordinate range of the
graph image being expanded or narrowed can be performed freely (Yes in
step S16→No in step S17→S18→S6).

Second Embodiment

[0098] FIGS. 10A to 10E are diagrams showing display operations (part 1)
of a second embodiment in a function graph display process of the graph
function calculator 10.

[0099] FIGS. 11A to 11E are diagrams showing display operations (part 2)
of the second embodiment in the function graph display process of the
graph function calculator 10.

[0100] When "Picture Graph" for creating a graph image composition screen
GK has been selected from a menu screen of operation modes displayed on
the color display unit 16 according to the operation of the MENU key of
the key input unit 11 and FILE has been specified from a menu displayed
at the lower end of the screen according to the operation of function key
Fn, a file selection screen G1 for selecting a desired file from "Images
& Coordinate setting & Graph formulas" files 1, 2 stored in the file
database 22F of the memory 22 is displayed as shown in FIG. 10A (step S1)

[0101] On the file selection screen G1, when file name BALL.g3m (FIG. 3)
desired by the user has been selected with cursor Cu and OPEN has been
specified by the operation of function key F1, an image in the selected
file BALL.g3m is read and written into the full color analysis image
memory 22g and is displayed as a background image on the color display
unit 16 as shown in FIG. 10B (step S2).

[0102] At this time, a graph coordinate system has not been displayed yet.

[0103] In addition, coordinate setting data in the selected file BALL.g3m
is read and set in the V-Window setting value memory 22c and SET UP data
memory 22d of the memory 22 (step S3).

[0104] At this time, a graph coordinate system corresponding to coordinate
setting data [coordinate range (Xmin=-0.15 to Xmax=6.15, Ymin=0 to
Ymax=3)] [scale values (X=0.5, Y=0.5)] [Grid: Line (line display)] [Axes:
On (scale display)] [Label: Off (no display of origin and coordinate axis
names x, y)] [V-W Lock: On (no range change)] (FIG. 3) set in the
V-Window setting value memory 22c and SET UP data memory 22d is written
in the color graph image memory 22h and is superimposed on the image of
BALL.g3m already displayed as a background image as shown in FIG. 10B.
The resulting image is displayed as a graph image composition screen GE
on the color display unit 16.

[0105] Next, graph formula data in the selected file BASKET.g3m is read
and set in the model formula memory 22e of the memory 22 (step S4).

[0106] When [GT] (switching between a graph and an formula) has been
specified according to the operation of function key F6 to analyze
trajectories b1 to b13 of a moving body (in this case, a ball) included
in the graph image composition screen GK from the graph, control is
passed to the graph formula input process of FIG. 6 (step SA). First, as
shown in FIG. 10C, a graph formula list screen G2 which lists the
individual graph formulas stored in the graph formula data memory 22b and
model formula memory 22e is displayed on the color display unit 16 (step
A1).

[0107] Here, when it has been determined that a model (model answer) has
been set because graph formula data Y2=PX2+QX+R (P=0.26 [allowable
range±0.06]: Q=1.6 [allowable range±0.2]: R=0.3 [allowable
range±0.2]) (FIG. 3) in the selected file BASKET.g3m has been set in
the model formula memory 22e (Yes in step A2), graph formula Y2 for the
model is displayed so as to be covered with mask M represented as
<<Model>> (step A3).

[0108] Then, if it has been determined that graph formula Y2
[Y2=PX2+QX+R] covered with the mask M is a graph with coefficients
(Yes in step A4), control goes into a state where a graph formula is to
be input according to a user operation.

[0109] Here, if graph formula Y1 [Y1=A sin B] the user came up with has
been input and displayed as shown in FIG. 10C on the basis of moving body
trajectories b1 to b13 on the graph image composition screen GK (FIG.
10B) displayed on the color display unit 16 according to steps S1 to S4,
the graph formula Y1 is stored in the graph formula data memory 22b (step
A9).

[0111] In this case, it has been determined that the former does not
coincide with the latter (No in step A10). Then, it is further determined
whether a function constituting a part of the user-input graph formula Y1
[Y1=A sin B] coincides with model (model answer) graph formula
Y2=PX2+QX+R stored in the model formula memory 22e (step A11).

[0112] In this case, too, it has been determined that the former does not
coincide with the latter (No in step A11) and a message "Different from
the Model Answer" AD informing the user that the user-input graph formula
Y1 [Y1=A sin B] differs from model (model answer) graph formula
Y2=PX2+QX+R stored in the model formula memory 22e is displayed in
red on the graph formula list screen G2 being displayed on the color
display unit 16 (step A12).

[0113] Here, if graph formula Y1 [Y1=AX2+B] has been input again by
the user and stored in the graph formula data memory 22b as shown in FIG.
10D (No in step A13→No in step A14→step A9), it is
determined that the function constituting a part of formula Y1 coincides
with the model (model answer) graph formula Y2=PX2+QX+R (Yes in step
A11).

[0114] Then, a message "Similar to the Model Answer" AS informing the user
that the reentered graph formula Y1 [Y1=AX2+B] is similar to model
(model answer) graph formula Y2=PX2+QX+R stored in the model formula
memory 22e is displayed in green on the graph formula list screen G2
being displayed on the color display unit 16 (step A15).

[0115] As shown in FIG. 10E, if graph formula Y1 [Y1=AX2+BX+C] has been
input again by the user and stored in the graph formula data memory 22b
(No in step A13→No in step A14→step A9), it is determined
that a part without the coefficients in graph formula Y1, that is,
Y1=quadratureX2+quadratureX+quadrature, coincides with model
(model answer) graph formula Y2=PX2+QX+R (Yes in step A10).

[0116] Then, a message "Equivalent to the Model answer" AE informing the
user that the graph formula Y1 [Y1=AX2+B+C] reentered again is
equivalent to model (model answer) graph formula Y2=PX2+QX+R is
displayed in blue on the graph formula list screen G2 being displayed on
the color display unit 16 (step A16).

[0117] As described above, equivalence information message AE about the
degree of coincidence, similarity information message AS, or difference
information message AD is displayed, depending on whether graph Y1 input
by the user excluding its coefficients, a function constituting a part of
graph Y1, or none of graph Y1 coincides with model (model answer) graph
formula Y2 corresponding to moving body trajectories b1 to b13 on the
background image.

[0118] Therefore, when a dynamic trajectory on an image is analyzed, the
user can enter a graph formula more similar to a correct graph formula,
while checking, from a message on the screen, the difference between the
user-input graph formula and its correct graph formula and therefore can
learn effectively.

[0119] Here, when cursor Cu is moved to the position of model graph
formula Y2 covered with mask M, mask M is erased and model graph formula
Y2 [Y2=PX2+QX+R] becomes visible and is set as a target formula in
graph display (Yes in steps A13→step A17).

[0120] Then, as shown in FIG. 11A, when the EXE key has been pressed, it
is determined that the input of the graph formula has been completed (Yes
in step A14) and that graph drawing has been specified (Yes in step S5).

[0121] Then, a graph coordinate system corresponding to coordinate setting
data (FIG. 3) in file No. 2 set in the V-Window setting value memory 22c
and SET UP data memory 22d is drawn again on the color graph image memory
22h. At the same time, graph Y1 corresponding to the user-input graph
formula Y1=AX2+BX+C (the initial values of coefficients A, B, C
being 0) is drawn in blue, the display color of graph Y1. Then, the image
of graph Y1 drawn on the color graph image memory 22h is superimposed on
the image of file No. 2 already drawn as a background image on the full
color analysis image memory 22g, thereby displaying the resulting image
as a graph image composition screen GK on the color display unit 16 (step
S6).

[0122] At this time, the user-input graph formula Y1=AX2+BX+C,
coefficient values [A=0, B=0, C=0], and variation [Step=0.1] are not
displayed.

[0123] Thereafter, when [Modify] has been specified according to the
operation of function key Fn from a function menu displayed at the lower
end of the screen according to the operation of the OPTN key (Yes in step
S19), graph formula Y1=AX2+BX+C specified on the graph formula list
screen G2 is displayed in blue, the display color of graph formula Y1. At
the same time, the initialized coefficient values [A=0, B=0, C=0] and
variation [Step=0.1] in the user coefficient value data memory 22f are
displayed (step S20).

[0125] Here, as shown in FIG. 11B, coefficient value [C=0] is specified
and displayed in red according to the operation of the ↑ cursor
key. At the same time, the specified coefficient value [C=0] is increased
in units of variation [Step=0.1] to [C=3] according to the repetitive
operation of the → cursor key or [C=3] is input directly by
operating a numeric key (step S22).

[0127] Then, as shown in FIG. 11C, coefficient value [A=0] is specified
and displayed in red according to the operation of the ↑ cursor
key. At the same time, the specified coefficient value [A=0] is decreased
in units of variation [Step=0.1] to [A=-0.3] according to the repetitive
operation of the  cursor key or [A=-0.3] is input directly by
operating a numeric key (No in step 24→No in step S25→step
S22).

[0129] Then, as shown in FIG. 11D, coefficient value [B=0] is specified
and displayed in red according to the operation of the ↓ cursor
key to make graph Y1 on the graph image composition screen GK more
similar to moving body trajectories b1 to b13. At the same time, the
specified coefficient value [B=0] is increased in units of variation
[Step=0.1] to [B=1.6] according to the repetitive operation of the
→ cursor key or [B=1.6] is input directly by operating a numeric
key (No in step 24→No in step S25→step S22).

[0131] At this time, the user can recognize that the blue graph Y1
corresponding to the user-input graph formula Y1=AX2+BX+C and
coefficient values [A=-0.3, B=1.6, C=3] has approximated moving body
trajectories b1 to b13 on the background image appreciably on the graph
image composition screen GK.

[0132] Then, to check how much the blue graph Y1 corresponding to the
user-input graph formula differs from graph Y2 corresponding to the model
answer graph formula, [Model] is specified according to the operation of
function key Fn from the function menu displayed at the lower end of the
screen according to, for example, the OPTN key as shown in FIG. 11E (Yes
in step S24).

[0133] Then, model (model answer) graph formula Y2=PX2+QX+R (P=-0.26:
Q=-1.6: R=0.3) stored in the model formula memory 22e is set as a target
formula in graph display (step S26) and the model graph formula
Y2=PX2+QX+R (P=-0.26: Q=1.6: R=0.3) is displayed in the set red on
the graph formula list screen G2 and graph Y2 corresponding to the model
graph formula is displayed in red (step S27).

[0134] Then, the difference between the coefficient values [A=-0.3, B=1.6,
C=3) of the user-input graph formula Y1=AX2+BX+C and the coefficient
values (P=-0.26: Q=1.6: R=0.3) of model graph formula Y2=PX2+QX+R is
calculated and it is determined on the basis of the allowable ranges
(P=-0.26±0.06: Q=1.6±0.2: R=0.3±0.2) previously set together
with the coefficient values of the model graph formula that the
difference between them has shown "coincidence," "similarity," or
"difference." According to this, a determination message of "similarity"
Si is added to coefficient value [A=-0.3] of the user-input graph formula
Y1=AX2+BX+C displayed on the graph image composition screen GK and a
determination message of "coincidence" Eq is added to each of coefficient
value [B=1.6] and coefficient value [C=3] on the screen (step S28).

[0135] As described above, when model (model answer) graph formula Y2
corresponding to moving body trajectories b1 to b13 on the background
image is coefficient-added graph formula Y2=PX2+QX+R in which
coefficient values and their allowable ranges (P=-0.26±0.06:
Q=1.6±0.2: R=0.3±0.2) are set and the user-input graph formula Y1
is graph formula Y1=AX2+BX+C which coincides with the graph formula
Y2 except for its coefficients, if the coefficient values
(A=quadrature, B=quadrature, C=quadrature) of the user-input graph
formula Y1=AX2+BX+C are input, they are compared with the
coefficient values of the model graph formula Y2 and their allowable
ranges and a determination message of "coincidence," "similarity," or
"difference" is displayed for each of the user-input coefficient values.

[0136] Therefore, when only the coefficient values in the user-input graph
formula differ from the correct graph formula, the user can enter
coefficient values closer to the coefficient values of the correct graph
formula, while checking the degree of the difference between the
coefficient values and the correct ones from a determination message on
the screen.

[0137] Accordingly, the user can learn effectively by making use of the
function of displaying the graph image composition screen GK obtained by
superimposing a graph image corresponding to the user-input graph formula
and a graph image corresponding to the correct graph formula on a
background image to be analyzed and the function of displaying a
determination message that the user-input graph formula is "equivalent
to," "similar to," or "different from" the correct graph formula.

[0138] The function of drawing graph Y2 corresponding to the model graph
formula by specifying [Model] according to the operation of function key
Fn from the function menu displayed at the lower end of the screen
according to the operation of the OPTN key and displaying graph Y2 as a
graph image composition screen GM can be performed not only in the
function of modifying a graph corresponding to the user-input graph
formula for which [Modify] has been specified, while increasing and/or
decreasing the coefficient values in the graph formula (steps S19 to S28)
but also in a state where the graph image composition screen GK is just
being displayed (step S6) (steps S29 to S31).

[0139] The operating methods of the graph function calculator 10 described
in the embodiments, that is, the individual methods including the
function graph display process explained in the flowcharts of FIGS. 4 and
5 and the graph formula input process accompanying the function graph
display process explained in the flowchart of FIG. 6, can be stored in an
external recording medium (23), such as a memory card (e.g., a ROM card
or a RAM card), a magnetic disk (e.g., a floppy disk or a hard disk), an
optical disk (e.g., a CD-ROM or a DVD), or a semiconductor memory, in the
form of programs the computer can execute. Then, the mediums can be
delivered. The processor (21) of the electronic calculator (10) loads the
program stored in the external recording medium (23) into the memory
(22). The computer is controlled by the read-in program, thereby
realizing the display function of the graph image composition screen GK
explained in the embodiments, which enables the same processes in the
aforementioned methods to be carried out.

[0140] Furthermore, the data of the programs which realize the above
methods can be transferred in the form of program code through a
communication network (public lines). The program data can be loaded by
communication devices (25) (30) connected to the communication network
into the processor (21) of the electronic calculator (10), thereby
realizing the display function of the graph image composition screen GK.

[0141] The invention is not limited to the above embodiments and, on the
basis of available skills in the present or future implementation phase,
may be practiced or embodied in still other ways without departing from
the spirit or character thereof. The embodiments include inventions of
different stages and therefore various inventions can be extracted by
combining suitably a plurality of structural requirements disclosed in
the embodiments. For example, even if some are removed from all of the
structural requirements shown in the embodiments or some structural
requirements are combined in a different mode, the resulting
configuration can be extracted as an invention, provided that the subject
to be achieved by the invention is accomplished and the effect of the
invention is obtained.

[0142] Additional advantages and modifications will readily occur to those
skilled in the art. Therefore, the invention in its broader aspects is
not limited to the specific details and representative embodiments shown
and described herein. Accordingly, various modifications may be made
without departing from the spirit or scope of the general inventive
concept as defined by the appended claims and their equivalents.